To my knowledge, there are two ways outside of past Mystery Gift events to obtain a Shiny Mew as of now. One is to access an old event location called Faraway Island in an Emerald copy. Inside Faraway Island is a Mew that you can soft reset in front of for a 1/8192 chance of being shiny.
Getting to Faraway Island almost certainly requires illegitimate means, but it is possible to teleport to the location on original hardware by usage of the Pomeg Glitch and it's "subglitch" Glitzer Popping.
It's also possible to get a Shiny Mew on a VC copy of Red & Blue on the 3DS. This process uses the 8F glitch and takes about ten hours. I'm not going to illustrate the method because this wonderful step-by-step guide will do a much better job at explaining if you are interested.
Shiny Mew has also been obtainable in Pokemon GO from time to time, so look out for those events if you are interested.
Hope this helps! Please ask if there are any more questions.
